Are there uses of linear logic in linguistics?

I've kind of heard of some applications but it's hard for me to see the big picture.

  • 2
    This is the course material from one of the courses I attended. I think your question is too broad to give a more concrete answer.
    – prash
    May 5 '15 at 19:12

Yes, linear logic has close connections with Lambek/categorial grammar. The big picture is basically that, with respect to a Lambek/categorial grammar, a proof of the syntactic category of a phrase of a language corresponds to a proof in the logical (e.g. deductive) sense, and that the grammar itself corresponds to a certain substructural logic. As Morrill (2011) puts it, "Technically, the Lambek calculus L is the multiplicative fragment of a non-commutative intuitionistic linear logic without empty antecedents."

A couple references:

  • Glynn V. Morrill. 2011. Categorial Grammar: Logical Syntax, Semantics, and Processing.

  • Richard Moot and Christian Retoré. 2012. The Logic of Categorial Grammars: A Deductive Account of Natural Language Syntax and Semantics.

Those deal mainly with syntax and talk a lot about linear logic. A good book dealing with semantics is Carpenter 1998, although his discussion of substructural logic (Ch. 5, sec. 4, pp. 169-170) is very limited.

  • Bob Carpenter. 1998. Type-Logical Semantics.

These references are full-length books. The original work developing linear logic, Lambek/categorial grammar, and their connections was mainly done in article form. The classic Lambek article is

  • Joachim Lambek. 1958. The Mathematics of Sentence Structure. The American Mathematical Monthly, 65(3), 154-170.

The connection between the Lambek calculus and natural deduction/substructural logic was, I think, first studied by Johan van Benthem. Consult the books above for specific and further references.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.